Problem: Rewrite as a simplified fraction. ${0.4\overline{82} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}1000x &= 482.8282...\\ 10x &= 4.8282...\end{aligned}}$ Subtracting the two equations, we have: ${990x = 478}$ ${x = \dfrac{478}{990}} $ ${x = \dfrac{239}{495}} $